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Theoretical Underpinnings of Singapore Math,[object Object],Sheraton San Diego Mission Valley Hotel, San Diego CA,[object Object],SingaporeMath.com,[object Object],Professional Development,[object Object],Please download from www.mathz4kidz.com,[object Object],Yeap Ban-Har, Ph.D.,[object Object],National Institute of Education,[object Object],Nanyang Technological University ,[object Object],Singapore,[object Object],banhar.yeap@nie.edu.sg,[object Object],DaQiao Primary School,[object Object]
Catholic High School (Primary),[object Object]
video of dice problem,[object Object],solving problems,[object Object],instructional models,[object Object],overview,[object Object],Bruner’s theory,[object Object],Skemp’s theory,[object Object],Dienes’ theory,[object Object]
introduction,[object Object],Wellington Primary School,[object Object]
Task,[object Object],Lesson Study Problem ,[object Object],Wellington Primary School,[object Object],Move 3 sticks to make 3 squares.,[object Object]
Task,[object Object],Move 3 sticks to make 3 squares.,[object Object]
Task,[object Object],Move 3 sticks to make 3 squares.,[object Object]
Task,[object Object],Move 3 sticks to make 2 squares.,[object Object]
Task,[object Object],Move 3 sticks to make 2 squares.,[object Object]
Task,[object Object],Move 3 sticks to make 2 squares.,[object Object]
A Problem from Singapore Grade 6 National Test,[object Object],Jim bought some chocolates and gave half of them to Ken. Ken bought some sweets and gave half of them to Jim. ,[object Object],Jim ate 12 sweets and Ken ate 18 chocolates. After that, the number of sweets and chocolates Jim had were in the ratio 1 : 7 and the number of sweets and chocolates Ken had were in the ratio 1 : 4. ,[object Object],How many sweets did Ken buy?,[object Object]
Jim bought some chocolates and gave half of them to Ken. Ken bought some sweets and gave half of them to Jim. Jim ate 12 sweets and Ken ate 18 chocolates. After that, the number of sweets and chocolates Jim had were in the ratio 1 : 7 and the number of sweets and chocolates Ken had were in the ratio 1 : 4. How many sweets did Ken buy?,[object Object],chocolates,[object Object],sweets,[object Object],Assuming that both boys did not have any sweet or chocolate before they bought the chocolates and sweets.,[object Object],12,[object Object],Jim,[object Object],12,[object Object],18,[object Object],12,[object Object],12,[object Object],12,[object Object],12,[object Object],Ken,[object Object],3 parts  12 + 12 + 12 + 12 + 18 = 66,[object Object],1 part  22,[object Object],Half of the sweets Ken bought = 22 + 12 = 34,[object Object],So Ken bought 68 sweets.`,[object Object]
88 children took part in a swimming competition.  1/3 of the boys and 3/7  of the girls wore swimming goggles. Altogether 34 children wore swimming goggles. ,[object Object],	How many girls wore swimming goggles on that day?,[object Object],A Problem from a Singapore Classroom,[object Object],Fairfield Methodist Primary School,[object Object]
[object Object],	How many girls wore swimming goggles on that day?,[object Object]
88,[object Object],34,[object Object],54,[object Object],[object Object],How many girls wore swimming goggles on that day?,[object Object]
34 – 20 = 14,[object Object],54 – 34 = 20,[object Object],34,[object Object],54,[object Object]
3 x 7 = 21,[object Object],21 girls wear goggles.,[object Object],A Curriculum That Helps Average Students Reach High Achievement,[object Object]
TIMSS 2007,[object Object],Trends in International Mathematics and Science Studies,[object Object],1995,[object Object],2003,[object Object],2007,[object Object],Grade 4,[object Object],Advanced,[object Object],38,[object Object],41,[object Object],38,[object Object],High,[object Object],70,[object Object],74,[object Object],73,[object Object],Intermediate,[object Object],89,[object Object],92,[object Object],91,[object Object],Low,[object Object],96,[object Object],98,[object Object],97,[object Object],North Vista Primary School,[object Object]
TIMSS 2007,[object Object],Trends in International Mathematics and Science Studies,[object Object],Average,[object Object],Indonesia,[object Object],Thailand,[object Object],Malaysia,[object Object],Singapore,[object Object],Grade 8,[object Object],Advanced,[object Object],2,[object Object],3,[object Object],0,[object Object],40,[object Object],2,[object Object],High,[object Object],15,[object Object],12,[object Object],4,[object Object],70,[object Object],18,[object Object],Intermediate,[object Object],46,[object Object],44,[object Object],14,[object Object],88,[object Object],50,[object Object],Low,[object Object],75,[object Object],66,[object Object],48,[object Object],97,[object Object],82,[object Object],Method Used in Singapore Textbooks,[object Object]
Beliefs,[object Object],Interest,[object Object],Appreciation,[object Object],Confidence,[object Object],Perseverance,[object Object],Monitoring of one’s own thinking,[object Object],Self-regulation of learning,[object Object],Attitudes,[object Object],Metacognition,[object Object],Numerical calculation,[object Object],Algebraic manipulation,[object Object],Spatial visualization,[object Object],Data analysis,[object Object],Measurement,[object Object],Use of mathematical tools,[object Object],Estimation,[object Object],Mathematical Problem Solving,[object Object],Reasoning, communication & connections,[object Object],Thinking skills & heuristics,[object Object],Application & modelling,[object Object],Skills,[object Object],Processes,[object Object],Concepts,[object Object],Numerical,[object Object],Algebraic,[object Object],Geometrical,[object Object],Statistical,[object Object],Probabilistic,[object Object],Analytical,[object Object],Mathematics Curriculum Framework,[object Object]
Every Child Counts,[object Object]
effective,[object Object],mathematics,[object Object],teaching,[object Object],BinaBangsa School, Indonesia,[object Object]
Primary Mathematics 1A,[object Object],Pedagogical Principle:,[object Object],Bruner,[object Object]
Number Bonds,[object Object],PCF Kindergarten TelokBlangah,[object Object]
Number Bonds,[object Object],PCF Kindergarten TelokBlangah,[object Object]
Bruner,[object Object],The concrete  pictorial  abstract approach is used to help the majority of learners to develop strong foundation in mathematics. ,[object Object],Division,[object Object],National Institute of Education,[object Object]
Division,[object Object],Princess Elizabeth Primary School,[object Object]
Catholic High School (Primary),[object Object]
mathz4kidz Learning Centre, Penang, Malaysia,[object Object],bruner’s theory,[object Object],concrete,[object Object],A lesson from Earlybird Kindergarten Mathematics,[object Object]
mathz4kidz Learning Centre, Penang, Malaysia,[object Object],concrete,[object Object],experiences,[object Object]
from,[object Object],concrete,[object Object],to,[object Object],pictorial,[object Object],mathz4kidz Learning Centre, Penang, Malaysia,[object Object]
from,[object Object],pictorial,[object Object],to,[object Object],abstract,[object Object],All Kids Are Intelligent Series,[object Object]
mathz4kidz Learning Centre, Penang, Malaysia,[object Object],symbols,[object Object]
using,[object Object],concrete,[object Object],materials,[object Object],Professional Development in AteneoGrade School, Manila, The Philippines,[object Object],Lesson Study in a Ministry of Education Seminar on Singapore Mathematics Teaching Methods in Chile,[object Object]
Primary Mathematics (Standards Edition) 2A,[object Object],Pictorial Before Abstract,[object Object]
     bruner,[object Object],Lesson Study in a Ministry of Education Seminar on Singapore Mathematics Teaching Methods in Chile,[object Object]
skemp’s,[object Object],theory,[object Object],conceptual,[object Object],understanding,[object Object],BinaBangsa School, Semarang, Indonesia,[object Object]
Keys Grade School, Manila, The Philippines,[object Object]
Keys Grade School, Manila, The Philippines,[object Object]
Skemp,[object Object],Understanding in mathematics  ,[object Object], relational,[object Object],  (conceptual) ,[object Object], instrumental  ,[object Object],  (procedural),[object Object], conventional  ,[object Object],Teaching for conceptual understanding is given emphasis in Singapore Math.,[object Object],Pedagogical Principle:,[object Object],Skemp,[object Object],Primary Mathematics Standards Edition Grade 6,[object Object]
Fraction Division,[object Object],Primary Mathematics Standards Edition Grade 6,[object Object]
skemp,[object Object],Scarsdale Middle School New York,[object Object]
Dienes,[object Object],Dienes encouraged the use of variation in mathematics education – perceptual variability and mathematical variability. ,[object Object],Pedagogical Principle:,[object Object],Dienes,[object Object],Primary Mathematics Standards Edition ,[object Object],Primary Mathematics Standards Edition Grade 1,[object Object]
Pedagogical Principle:,[object Object],Dienes,[object Object],Primary Mathematics Standards Edition Grade 1,[object Object]
Pedagogical Principle:,[object Object],Dienes,[object Object],Primary Mathematics Standards Edition Grade 2,[object Object]
homework,[object Object],Are you able to see how these tasks are varied according to Dienes’ idea of mathematical variability? ,[object Object]
How is Task 4 different from Task 5?,[object Object],16,[object Object],Primary Mathematics Standards Edition Grade 5,[object Object]
16,[object Object],What is the given in Task 5? What is the given in Task 6? Are these different?,[object Object],30,[object Object],Primary Mathematics Standards Edition Grade 5,[object Object]
Earlybird Kindergarten  Mathematics ,[object Object],Standards Edition ,[object Object],Can you see how Dienes’ idea is used in designing these tasks?,[object Object],diene’s,[object Object],theory,[object Object],of,[object Object],variation,[object Object]
  dienes,[object Object],Princess Elizabeth Primary School, Singapore,[object Object]
Emphasis on pictorial representation and systematic variation to enhance conceptual understanding,[object Object]
conclusion,[object Object],PCF Kindergarten PasirRis,[object Object]
Instructional Models,[object Object],[object Object]
 Modeling
 Providing
ExplaningDaQiao Primary School,[object Object]
“Children are trulythe future of our nation. “,[object Object],Irving Harris,[object Object]

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Professional Development for Californian Teaching Teaching Singapore Math

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